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If the sum of two numbers is 36 and their HCF and LCM are 3 and 105 respectively, the sum of the reciprocals of the numbers is = ?

1²/₃₅
2³/₃₅
3⁴/₃₅
4None of these

Answer:- 1

Explanation:-

Solution:

Let the number be a and b

\begin{aligned} Then, \\ a + b = 36 & \\ a b = 3 \times 105 = 315 \\ ∴ Required sum \\ = \frac{1}{a} + \frac{1}{b} \\ = \frac{a + b}{a b} \\ = \frac{36}{315} \\ = \frac{4}{35} \end{aligned}

$\eqalign{ & {\text{Then,}} \cr & a + b = 36\& \cr & ab = 3 \times 105 = 315 \cr & \therefore {\text{Required sum}} \cr & {\text{ = }}\frac{1}{a} + \frac{1}{b} \cr & = \frac{{a + b}}{{ab}} \cr & = \frac{{36}}{{315}} \cr & = \frac{4}{{35}} \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the number be a and b

\begin{aligned} Then, \\ a + b = 36 & \\ a b = 3 \times 105 = 315 \\ ∴ Required sum \\ = \frac{1}{a} + \frac{1}{b} \\ = \frac{a + b}{a b} \\ = \frac{36}{315} \\ = \frac{4}{35} \end{aligned}

$\eqalign{ & {\text{Then,}} \cr & a + b = 36\& \cr & ab = 3 \times 105 = 315 \cr & \therefore {\text{Required sum}} \cr & {\text{ = }}\frac{1}{a} + \frac{1}{b} \cr & = \frac{{a + b}}{{ab}} \cr & = \frac{{36}}{{315}} \cr & = \frac{4}{{35}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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